Question

The graph of r=-14 cos theta has which of the following characteristics?

Answer 1

A

Explanation:

Answer 2

A

Explanation:

Use formulas:

`r=√(x^2+y^2),`

`\cos \theta=(x)/(√(x^2+y^2)).`

Substitute them into the equation
`r=-14\cos \theta:`

`√(x^2+y^2)=-14\cdot (x)/(√(x^2+y^2)).`

Multiply this equation by
`√(x^2+y^2):`

`x^2+y^2=-14x.`

Now rewrite this equation as

`x^2+14x+y^2=0,\\ \\x^2+14x+49-49+y^2=0,\\ \\(x+7)^2+y^2=49.`

This is the equation of the circle with center at point (-7,0) and radius r=7 (diameter 14).